Question

10-14 solve the following equations

10. -sin^2 x=2cosx-2
11. 2sin(2x)-2sinx+2sqrt3cosx-sqrt3=0
12. csc(4x)-2=0
13. cos^2(2x)-sin^2(2x)=0
14. sin(2x)=sinx

Answer 1

10. sin^2 x = 1- cos^2 x substitute this you get : -1+cos^2 = 2cosx-2
bring it to one side you get: cos^2 - 2cosx +1 = 0 (this reminds you of x^2 + x + c right?

Answer 2

(cosx -1)(cosx +2) = 0 -> cos x = 1 or cosx =-2;

Answer 3

11-14

Answer 4

11. Rule: sin 2x = 2sinx.cosx ; sub: 4sinxcox - 2sinx + 2sqrt3cox-sqrt3 = 0; //no clue yet
14. 2sinxcox = sinx; 2cosx = 1 -> cosx= 1/2;

Answer 5

12-13